The setup and the solver here are the ones used in ONS2021 with the addition of stratification. Both simulations solve the three-dimensional Navier-Stokes with the Boussinesq approximation in cylindrical coordinates. The solver uses a third-order Runge-Kutta method combined with second-order Crank-Nicolson to advance the equations in time. Second-order-accurate central differences are used for the spatial derivatives in a staggered grid. A wall-adapting local eddy viscosity (WALE) is used to properly capture the turbulent boundary layer dynamics [1]}. Both the BI and BE simulations use Dirichlet boundary conditions at the inflow, convective outflow and Neumann at the radial boundary. Similarly to [2]} a sponge layer is added to the boundaries to avoid the spurious reflection of gravity waves.
